The paper presents a spectral formulation of surface profile irregularity in a wideband frequency range for roughness, waviness and shape components along the measured length. A unique distribution of roughness and waviness components is proposed, according to the nature of their origination in the course of machining with tools of defined cutting edge, as distinct from standard filtration in measurements of surface irregularities. Differences resulting from both formulations are outlined as well as the method of determining the frequency of component separation for surface roughness and waviness.

Local geometric deviations of free-form surfaces are determined as normal deviations of measurement points from the nominal surface. Different sources of errors in the manufacturing process result in deviations of different character, deterministic and random. The different nature of geometric deviations may be the basis for decomposing the random and deterministic components in order to compute deterministic geometric deviations and further to introduce corrections to the processing program. Local geometric deviations constitute a spatial process. The article suggests applying the methods of spatial statistics to research on geometric deviations of free-form surfaces in order to test the existence of spatial autocorrelation. Identifying spatial correlation of measurement data proves the existence of a systematic, repetitive processing error. In such a case, the spatial modelling methods may be applied to fitting a surface regression model representing the deterministic deviations. The first step in model diagnosing is to examine the model residuals for the probability distribution and then the existence of spatial autocorrelation.